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|   | '''Note on notation.'''  When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:  |   | '''Note on notation.'''  When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:  | 
|   |  |   |  | 
| − | :{| cellpadding=4
  | + | {| align="center" cellspacing="6" width="90%"  | 
| − | | ''J''<sub>''OS''</sub>  | + | |  | 
| − | | = || ''Den''(''L''<sub>''J'' </sub>)
  | + | <math>\begin{array}{lclclclcl}  | 
| − | | = || ''Proj''<sub>''OS'' </sub>''L''<sub>''J''</sub>
  | + | J_{OS}  | 
| − | | = || (''L''<sub>''J'' </sub>)<sub>''OS''</sub>
  | + | & = & \operatorname{Den}(L_J)  | 
| − | | = || ''L''(''J'')<sub>''OS''</sub>
  | + | & = & \operatorname{proj}_{OS} L_J  | 
| − | |-
  | + | & = & (L_J)_{OS}  | 
| − | | ''J''<sub>''SI''</sub>
  | + | & = & L(J)_{OS}  | 
| − | | = || ''Con''(''L''<sub>''J'' </sub>)
  | + | \\[6pt]  | 
| − | | = || ''Proj''<sub>''SI'' </sub>''L''<sub>''J''</sub>
  | + | J_{SI}  | 
| − | | = || (''L''<sub>''J'' </sub>)<sub>''SI''</sub>
  | + | & = & \operatorname{Con}(L_J)  | 
| − | | = || ''L''(''J'')<sub>''SI''</sub>
  | + | & = & \operatorname{proj}_{SI} L_J  | 
| − | |-
  | + | & = & (L_J)_{SI}  | 
| − | | ''J''<sub>''OI''</sub>
  | + | & = & L(J)_{SI}  | 
| − | | = || ''Int''(''L''<sub>''J'' </sub>)
  | + | \\[6pt]  | 
| − | | = || ''Proj''<sub>''OI'' </sub>''L''<sub>''J''</sub>
  | + | J_{OI}  | 
| − | | = || (''L''<sub>''J'' </sub>)<sub>''OI''</sub>
  | + | & = & \operatorname{Int}(L_J)  | 
| − | | = || ''L''(''J'')<sub>''OI''</sub>
  | + | & = & \operatorname{proj}_{OI} L_J  | 
|   | + | & = & (L_J)_{OI}  | 
|   | + | & = & L(J)_{OI}  | 
|   | + | \end{array}</math>  | 
|   | |}  |   | |}  | 
|   |  |   |  |